论文标题
全球拓扑功能优化的快速稳固的方法
A Fast and Robust Method for Global Topological Functional Optimization
论文作者
论文摘要
拓扑统计数据以持久图的形式是一类形状描述符，可在数据中捕获全局结构信息。从数据结构到持久图的映射几乎无处可区分，从而使拓扑梯度可以反向传播到普通梯度。但是，作为优化拓扑功能的一种方法，这种反向传播方法是昂贵，不稳定且产生非常脆弱的Optima的方法。我们的贡献是引入一种新型的返回方案，该方案明显更快，更稳定，并且产生更强大的Optima。此外，该方案还可以用来在持久图中产生对点的稳定可视化，以作为数据结构中关键和近距离简单的分布。
Topological statistics, in the form of persistence diagrams, are a class of shape descriptors that capture global structural information in data. The mapping from data structures to persistence diagrams is almost everywhere differentiable, allowing for topological gradients to be backpropagated to ordinary gradients. However, as a method for optimizing a topological functional, this backpropagation method is expensive, unstable, and produces very fragile optima. Our contribution is to introduce a novel backpropagation scheme that is significantly faster, more stable, and produces more robust optima. Moreover, this scheme can also be used to produce a stable visualization of dots in a persistence diagram as a distribution over critical, and near-critical, simplices in the data structure.
